Simulating Downhole Flow Through a Perforation

ABSTRACT

A method of testing a core sample is provided. The method comprises determining an impedance map, attaching a sleeve to the core sample, and measuring a flow performance of the core sample. An impedance of each of a plurality of portions of the sleeve is based on the impedance map.

CROSS-REFERENCE TO RELATED APPLICATIONS

None.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not applicable.

REFERENCE TO A MICROFICHE APPENDIX

Not applicable.

BACKGROUND

Hydrocarbons may be produced from wellbores drilled from the surfacethrough a variety of producing and non-producing formations. Thewellbore may be drilled substantially vertically or may be an offsetwell that is not vertical and has some amount of horizontal displacementfrom the surface entry point. In some cases, a multilateral well may bedrilled comprising a plurality of wellbores drilled off of a mainwellbore, each of which may be referred to as a lateral wellbore.Portions of lateral wellbores may be substantially horizontal to thesurface. In some provinces, wellbores may be very deep, for exampleextending more than 10,000 feet from the surface.

A variety of servicing operations may be performed on a wellbore afterit has been initially drilled. A lateral junction may be set in thewellbore at the intersection of two lateral wellbores and/or at theintersection of a lateral wellbore with the main wellbore. A casingstring may be set and cemented in the wellbore. A liner may be hung inthe casing string. The casing string may be perforated by firing aperforation gun or perforation tool. A packer may be set and a formationproximate to the wellbore may be hydraulically fractured. A plug may beset in the wellbore.

Perforation tools may comprise explosive charges that are detonated tofire the perforation tool, perforate a casing if present, and createperforations and/or tunnels into a subterranean formation proximate tothe wellbore. The tunnels into the subterranean formation may besurrounded by an envelope or layer of crushed material. The crushedmaterial may shift and/or flow into the tunnels, clogging the tunnels tosome extent, or may realign and reduce the permeability of the formationproximate to the tunnels. A variety of perforation tool designparameters can be adjusted with the intention of encouraging desiredresults and mitigating undesired results of the perforation. A densityof shots into the subterranean formation can be adjusted. An angle ofthe focus axis of the explosive charges can be adjusted to angle up, toangle down, or to angle normal to the axis of the perforation tool.Parameters of the explosive charge itself may be altered to adapt todifferent downhole parameters.

Sometimes downhole perforation procedures are conducted with pre-firingwellbore pressure maintained below the formation fluid pressure, whichmay be referred to as an under balanced condition, or maintained abovethe formation fluid pressure, which may be referred to as an overbalanced condition. Sometimes a tool may be carried with the perforationtool or incorporated into the perforation tool to create a transientfluid surge after firing of the perforation tool to supplement orprolong an under balanced condition. The perforation procedure may bedesigned to adapt to different perforation conditions based onestimations and/or projections of downhole parameters. For example, apre-firing wellbore pressure may be calculated to provide a specificintensity of under balance or over balance. In the case an under balancecondition is desired, a volume of fluid surge may be calculated.

In order to design the perforation tool and/or a downhole perforationprocedure, one or more core samples that are considered to berepresentative of the subterranean formation to be perforated may betested to determine some parameters of the subterranean formation and/orinteractions between the explosive charges and the subterraneanformation. The evaluations of test results may be used in designing theperforation tool and/or the downhole perforation procedure.

SUMMARY

In an embodiment, a method of testing a core sample is disclosed. Themethod comprises determining an impedance map, attaching a sleeve to thecore sample, and measuring a flow performance of the core sample. A flowimpedance of each of a plurality of portions of the sleeve is based onthe impedance map.

In an embodiment, a perforation test target is disclosed. Theperforation test target comprises a metal plate, a core sample adheredto the metal plate at one end, and a first sleeve adhered to the coresample. A flow impedance of each of a plurality of portions of the firstsleeve is based on a predetermined impedance map.

In an embodiment, a system for testing a core sample is disclosed. Thesystem comprises a non-permeable sleeve placed over the core sample, afirst pair of opposing actuators to apply opposing force to thenon-permeable sleeve in a first axis normal to the axis of the coresample, and a second pair of opposing actuators to apply opposing forceto the non-permeable sleeve in a second axis normal to the axis of thecore sample and normal to the first axis. The system further comprises awellbore pressure reservoir to provide simulated wellbore pressure and aformation pressure reservoir to provide simulated formation fluidpressure.

In an embodiment, a perforation test target is disclosed. Theperforation test target comprises a metal plate and a core sampleadhered to the metal plate at one end, wherein the core sample has theshape of an elliptic cylinder. In an embodiment, a major radius of across-section of the core sample is at least 1.1 times a minor radius ofthe cross-section of the core sample. In an embodiment, the perforationtest target further comprises a sleeve adhered to the core sample,wherein a flow impedance of each of a plurality of portions of thesleeve is based on an impedance map. In an embodiment, the impedance mapis determined based on at least one of a formation parameter, aperforation parameter, a wellbore parameter, and a core sampleparameter.

These and other features will be more clearly understood from thefollowing detailed description taken in conjunction with theaccompanying drawings and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the present disclosure, referenceis now made to the following brief description, taken in connection withthe accompanying drawings and detailed description, wherein likereference numerals represent like parts.

FIG. 1 is an illustration of a small scale test fixture according to anembodiment of the disclosure.

FIG. 2 is an illustration of a core sample and an impedance sleeveaccording to an embodiment of the disclosure.

FIG. 3 is an illustration of a core sample and an impedance sleevemanufactured in the form of a sheet according to an embodiment of thedisclosure.

FIG. 4A is an illustration of an impedance sleeve manufactured as asheet comprising layers of impedance material according to an embodimentof the disclosure.

FIG. 4B is an illustration of an impedance sleeve manufactured as asheet according to an embodiment of the disclosure.

FIG. 4C is an illustration of an impedance sleeve manufactured as asheet according to an embodiment of the disclosure.

FIG. 5 is an illustration of a core sample having an ellipticalcross-section according to an embodiment of the disclosure.

FIG. 6A is an illustration of a variable compliance sleeve according toan embodiment of the disclosure.

FIG. 6B is an illustration is an illustration of a variable compliancesleeve in a test configuration according to an embodiment of thedisclosure.

FIG. 7 is an illustration of a core sample test fixture suitable forproviding overburden pressure according to an embodiment of thedisclosure.

FIG. 8 is an illustration of a core sample text fixture suitable forproviding overburden pressure according to an embodiment of thedisclosure.

FIG. 9 is an illustration of a method of testing a core sample accordingto an embodiment of the disclosure.

FIG. 10 is an illustration of a method of testing a core sample,determining perforation gun design parameters and/or perforationprocedure parameters, and perforating a wellbore according to anembodiment of the disclosure.

FIG. 11 is an illustration of a wellbore, a conveyance, and aperforation tool according to an embodiment of the disclosure.

DETAILED DESCRIPTION

It should be understood at the outset that although illustrativeimplementations of one or more embodiments are illustrated below, thedisclosed systems and methods may be implemented using any number oftechniques, whether currently known or in existence. The disclosureshould in no way be limited to the illustrative implementations,drawings, and techniques illustrated below, but may be modified withinthe scope of the appended claims along with their full scope ofequivalents.

Unless otherwise specified, any use of any form of the terms “connect,”“engage,” “couple,” “attach,” or any other term describing aninteraction between elements is not meant to limit the interaction todirect interaction between the elements and may also include indirectinteraction between the elements described. In the following discussionand in the claims, the terms “including” and “comprising” are used in anopen-ended fashion, and thus should be interpreted to mean “including,but not limited to . . . ”. Reference to up or down will be made forpurposes of description with “up,” “upper,” “upward,” or “upstream”meaning toward the surface of the wellbore and with “down,” “lower,”“downward,” or “downstream” meaning toward the terminal end of the well,regardless of the wellbore orientation. The term “zone” or “pay zone” asused herein refers to separate parts of the wellbore designated fortreatment or production and may refer to an entire hydrocarbon formationor separate portions of a single formation such as horizontally and/orvertically spaced portions of the same formation. The variouscharacteristics mentioned above, as well as other features andcharacteristics described in more detail below, will be readily apparentto those skilled in the art with the aid of this disclosure upon readingthe following detailed description of the embodiments, and by referringto the accompanying drawings.

Testing of core samples is conducted to evaluate and to adjustperforation gun design parameters and perforation procedure parameters.Testing may be conducted based on American Petroleum Institute (API)reference procedure 19B (API RP 19B). Testing is typically performed ona circular cylinder core sample that is considered to be representativeof the subterranean formation that is to be perforated. One end of thecore sample is adhered to a metal plate representing a wellbore casing.An explosive charge is placed proximate to and focused on the metalplate and the core sample. A pressure is applied to the housingcontaining the explosive charge and/or the metal plate to model thewellbore pressure. Pressure is applied to the core sample surfaces thatare not adhered to the metal plate to model one or more of formationoverburden pressure (static pressure from the rock matrix exerted on anysubject volume of the formation) and formation fluid pressure (pressurefrom hydrocarbons such as oil, gas, and/or water that may be a staticpressure prior to perforation but may be dynamic pressure afterperforation as the fluids flow). In some contexts, formation fluidpressure may be referred to as pore pressure and/or formation porepressure.

An explosive charge, for example a shaped explosive charge suitable forassembling into a perforation gun, is detonated, perforating the metalplate, perforating the core sample, leaving a perforation tunnelenveloped by a layer of crushed rock in the core sample. After theexplosive charge is fired, the fluid pressure desirably causes fluidflow into the tunnel and out the perforation hole in the metal plate.During the test, various pressures and flows are measured and recordedfor post-test evaluation. After the test, the core sample may be removedfrom the test fixture, split and/or sawed open, and the perforationtunnel and crush zone geometry measured and evaluated.

In one test, which may be referred to as a radial target test, the coresample may be tested to measure radial flow, fluid flow from theformation across a circumferential boundary of the core sample andthrough an end of the core sample. In another test, which may bereferred to as an axial target test, the core sample may be tested tomeasure axial flow, fluid flow from the formation across a boundarydefined by the end of the core sample opposite the metal plate. In thesetwo tests, however, a number of the test conditions differ significantlyfrom the downhole environment that the testing is intended to model. Thepresent disclosure teaches several innovations any one of which maycontribute to more faithfully model the downhole environment and maypromote improved perforation design and improved perforation proceduredesign based on the results of the more realistic testing.

In the radial target test, a constant fluid pressure is applied acrossthe surfaces of the core sample not adhered to the metal plate. Thisdiffers from the downhole environment in that, after perforation andwhen fluid flows into the perforation tunnels, a fluid pressuredistribution is present across the circumferential surface of thecorresponding volume in the downhole environment, that is, the fluidpressure is different at different points or locations on thecircumferential surface and/or at the end. This fluid pressure maydiffer with displacement axially from one end of the correspondingvolume to the other end of the corresponding volume as well ascircumferentially around the corresponding volume.

In the axial target test, a constant fluid pressure is applied to theend of the core sample opposite the metal plate to model formation fluidpressure. An impermeable sleeve may be placed around the circumferenceof the core sample to prevent fluid flow through the circumferentialsurface of the core sample.

The present disclosure teaches a plurality of different innovations forproviding more faithful modeling of the downhole environment in thetesting laboratory. It is contemplated that some of the disclosedembodiments may desirably be used in combination, but several of theinnovations may suitably be employed separately from the otherinnovations. These innovations are briefly sketched here but aredescribed in detail supported by the corresponding drawings. In anembodiment, an impedance sleeve is placed over the core sample prior toradial target testing, wherein the flow impedance of each of a pluralityof portions of the sleeve may be different, based on an impedance map.The impedance map may be determined, for example, based on any of one ormore formation parameters, one or more perforation gun parameters, oneor more wellbore parameters, and one or more core sample parameters.After detonation of the explosive charge, fluid may flow across theimpedance sleeve, through the core sample, and into the perforation. Inthe presence of fluid flow, the impedance sleeve transforms the constantambient pressure applied to the outside of the impedance sleeve to avariety of different fluid pressure values incident on the surface ofthe core sample, based on the different flow impedances of the portionsof the sleeve. The flow impedance of each of the portions of the sleevemay be collectively referred to as an impedance distribution of thesleeve. This impedance distribution can be calculated based on known orestimated parameters, and the sleeve manufactured according to theimpedance distribution and/or the impedance map.

In an embodiment, the impedance sleeve may be combined with anelliptical cylinder core sample. The elliptical cross-section of thecore sample can be adapted to provide a desired difference of pressurearound an internal circular cross-section of the core sample byselecting an appropriate ratio between major radius and minor radius ofthe elliptical cross-section, for example a ratio of 1.1 to 1, 2 to 1,or some other effective ratio, in accordance with the ratio ofpermeability anisotropy of the core sample material. When combined withsuch an elliptical cylinder core sample, the impedance sleeve may bemanufactured to have flow impedance varying only in the axial direction,possibly reducing the complexity of manufacturing the impedance sleeveand of mounting the impedance sleeve over the core sample. A core samplelathed to have a generally and/or substantially elliptic cylinder shapeis thought to be novel and to have applicability in testingindependently of the impedance sleeve.

In an embodiment, a compliant sleeve having compliance that varies inthe radial direction may be placed over a core sample assembly.Mechanical compliance, the compliance referred to herein, may be definedas the inverse of mechanical stiffness. The compliance of each of aplurality of different portions of the compliance sleeve may havedifferent values at different locations on a perimeter of across-section of the core sample that is normal to the axis of the coresample, may be placed over a core sample assembly. A constant overburdenpressure applied to the compliant sleeve is transformed by the compliantsleeve into a pressure that varies in the radial direction applied tothe core sample assembly. At a portion of the compliant sleeve where thecompliance is reduced, less of the overburden pressure is transferred tothe core sample assembly; at a portion of the compliant sleeve where thecompliance is greater, more of the overburden pressure is transferred tothe core sample assembly.

In an embodiment, a test fixture is contemplated having two pairs ofopposing actuators to apply forces in the horizontal and the verticaldirections to a core sample to model overburden pressure in thehorizontal and vertical axes. In an embodiment, the force applied by thetwo pairs of opposing actuators may be controlled separately in thehorizontal and the vertical directions, for example to model adifference between vertical overburden pressure and horizontaloverburden pressure. The actuators may be hydraulically actuated orelectrically actuated.

Turning now to FIG. 1, a test system 100 is described. The system 100comprises a core sample 102, an impedance sleeve 104, a metal plate 106,a first pressure chamber 108, a first pump 110, a second pump 112, and afirst pressure accumulator 114. The metal plate 106 may be a section ofcasing, such as casing approximating that used in the wellbore to beperforated. Additionally, cement (not shown) may be located between themetal plate 106 and the core sample 102, such as cement approximatingthe cement used in the wellbore to be perforated. The system 100 furthercomprises an explosive charge 116, a second pressure chamber 118, athird pump 120, and a second pressure accumulator 122. A variety ofmeasurement and sensing equipment (not shown) may be coupled to thesystem 100 to measure fluid pressures, fluid flows, and other conditionsbefore, during, and after the detonation of the explosive charge 116.Likewise, a variety of control equipment (not shown) may be coupled tothe system 100 to trigger the detonation of the explosive charge 116, tocontrol the pumps 110, 112, 120, and to control other test apparatus. Indifferent embodiments, the system 100 may have different componentsand/or arrangements of components than that illustrated in FIG. 1. Insome contexts, the assembly of the core sample 102, the impedance sleeve104, and the metal plate 106 may be referred to as a perforation testtarget.

The first pump 110 is plumbed by tubing to the first pressure chamber108 and provides pressure, for example, to model formation overburdenpressure. In some test configurations, formation overburden pressure maynot be modeled, and the first pump 110 may be omitted from the system100 in this circumstance.

The second pump 112 is plumbed by tubing to the end of the core sample102. The second pump 112 may provide fluid pressure and fluid flow tomodel formation fluid pressure and fluid flow after the perforation hasoccurred. In an embodiment, the core sample 102 and impedance sleeve 104may be enclosed within an impermeable bladder (not shown) that separatesthe first pressure chamber 108 from the core sample 102 and impedancesleeve 104, and the second pump 112 may provide pressure to the interiorof this impermeable bladder. In an embodiment, proppant material may bedisposed between the impermeable bladder and the impedance sleeve 104.The second pump 112 is also plumbed by tubing to the first pressureaccumulator 114. The first pressure accumulator 114 mitigates pressuretransients during fluid flow transients.

The explosive charge 116 is similar to or identical to an explosivecharge that may be deployed in a perforation gun. The explosive charge116 may be enclosed in a housing for use in core sample testing, wherethe free volume inside the housing is adapted to model the free volumeinside the simulated perforation gun. The explosive charge 116 maycomprise a liner, an outer shell, and a shaped charge between the linerand the outer shell. The explosive charge 116, when detonated, producesan intense energetic jet focused along the axis of the explosive charge116. The energetic jet perforates the metal plate 106, perforates thecement, and perforates the core sample 102. Depending on the explosivecharge 116 employed, the diameter of the perforation in the metal plate106, the depth of the tunnel, the diameter of the tunnel, and thediameter of the zone of crushed rock surrounding the tunnel produced bydetonation of the explosive charge 116 may vary. The diameter of theperforation in the metal plate 106, the depth of the tunnel, thediameter of the tunnel, and the diameter of the zone of crushed rock maybe referred to in some contexts as perforation geometry. It may be oneof the objectives of testing to evaluate the effects of differentexplosive charges 116 on the core sample 102. A series of tests may beconducted with different explosive charges 116 to identify a suitablematch of the design of the explosive charge 116 to the core sample 102.

The third pump 120 is plumbed by tubing to the second pressure chamber118 and provides pressure, for example, to model wellbore pressure. Thethird pump 120 is also plumbed by tubing to the second pressureaccumulator 122. The second pressure accumulator 122 mitigates pressuretransients during fluid flow transients. The pressure supplied by thethird pump 120 may be regulated to provide an under balanced pressure,an over balanced pressure, or a balanced pressure prior to detonatingand/or firing the explosive charge 116. In an embodiment, the secondpressure accumulator 122 may be replaced by a surge apparatus to promotesurging the second pressure chamber 118 after the perforation, forexample to produce or sustain an under balance pressure in the secondpressure chamber 118.

In an embodiment, the first pressure accumulator 114 may be replaced bya surge device. For example, a surge device having a piston, apressurized gas chamber, a low pressure chamber, and a crushable springdesigned to provide a specific pressure transient after perforation maybe used. For further details of an exemplary surge device, see U.S. Pat.No. 4,805,726. When activated, for example shortly after the explosivecharge 116 is detonated, the pressurized gas chamber, previouslyisolated from the low pressure chamber, is admitted to the low pressurechamber through an orifice. The decreased pressure of the pressurizedgas chamber allows the piston to be forced back onto the crushablespring by an in-flow of fluid. The mass of the piston, the properties ofthe crushable spring, the internal volume of the pressurized gas chamberand of the low pressure chamber, the diameter of an orifice between thepressurized gas chamber and the low pressure chamber can be selected toprovide a desirable pressure transient. The pressure transient thatoccurs in the absence of the surge device may be measured in a previousiteration of core sample testing. Alternatively, the pressure transientthat occurs in the absence of the surge device may be determined bysimulation and/or calculations. A desired pressure transient may bedetermined that differs from the pressure transient that occurs in theabsence of the surge device, and the piston mass, the volume of theinterior chamber, and the spring constant of the crushable spring may bedesigned and/or selected to produce the desired pressure transient.Activating the surge device to accept a sudden in-flow of fluid duringthe pressure transient that results from perforation, to perform asurge, is said to modify the pressure transient and/or to shape thepressure transient. The surge device may be said to modify the pressuretransient and/or to produce a modified pressure transient.

In an embodiment, the surge device coupled to the second pump 112 maypromote simulating a transient cleanup flow, for example a pressuretransient that may be limited to about 10 milliseconds, about 100milliseconds, about 300 milliseconds, about 1 second, or some othertransient time interval. By providing a transient reduction in pressureincident on the impedance sleeve 104, the effect of a transient periodof clean-up of the crush zone after perforation may be created. In anembodiment, the second pressure accumulator 122 may be replaced by asurge device such as that described above having a piston, a crushablespring, a high pressure gas chamber, a low pressure gas chamber in orderto provide tuning and/or adaptation of the transient pressure in thesecond pressure chamber 118. Likewise, when used in conjunction with thesecond pressure chamber 118, the surge device may be used to shape thewellbore pressure transient to simulate downhole conditions afterperforation has occurred.

Turning now to FIG. 2, further details of the impedance sleeve 104 aredescribed. In an embodiment, the impedance sleeve 104 may be comprisedof a tubular portion 140 that is slipped over the outside of the coresample 102 and further comprised of a cap portion 142 that is placed onthe end of the core sample 102 and overlapping or adjacent to the end ofthe installed tubular portion 140. The tubular portion 140 and the capportion 142 may be manufactured of filter material, for exampledifferent layers of filter paper as described further below, or ofvariable thickness ceramic. In some contexts, the variable thickness ofthe ceramic sleeve may be referred to as a geometry of the ceramicsleeve. The tubular portion 140 and/or the cap portion 142 may becomprised of fine particle materials, for example a filter cakecomprised of fine particle materials, for example fine silt, fine sand,fine clay, and other fine particles. The selection of particles,selection of materials, the thickness of the filter cake, the method ofmanufacturing the filter cake may be adapted to produce the impedancesleeve 104, or the tubular portion 140 and/or the cap portion 142,having the desired flow impedance at each portion of impedance sleeve104.

The tubular portion 140 may be manufactured to fit the core sample 102snuggly, to avoid any fluid infiltrating under the ends of the tubularportion 140 rather than passing through the outer surface of the tubularportion 140. In an embodiment, the ends of the tubular portion 140 maybe secured to the core sample 102, for example using snap rings, clamps,wires, strings, and/or other attaching hardware. In an embodiment, thetubular portion 140 may be adhered to the core sample 102, for exampleat a limited number of interior areas of the tubular portion 140 so asto avoid the interference of the adhesive with the predeterminedimpedance of the tubular portion 140. Alternatively, the impedancesleeve 104 may be secured to the core sample 102 by a support sleevethat is highly permeable and functions to hold the impedance sleeve 104in place and mitigate fluid infiltrating under the ends of the tubularportion 140. In an embodiment, the tubular portion 140 may be slippedover the core sample 102, and the core sample 102 and the adjacent endof the tubular portion 140 may then be cemented to the metal plate 106,thereby securing the end of the tubular portion 140 proximate to themetal plate 106.

In an embodiment, the flow impedance of the cap portion 142 may beconstant across the cap portion 142. Alternatively, in anotherembodiment, the flow impedance of the cap portion 142 may vary from thecenter of the cap portion 142 out to the edges of the cap portion 142,for example having a greater flow impedance towards the curved perimeterof the end cap 142 and a lesser flow impedance towards the center of theend cap 142.

The tubular portion 140 is manufactured so that different portions,parts, or areas of the tubular portion 140 may have different values offlow impedance. In some contexts, the tubular portion 140 may be said tohave an impedance distribution, meaning a variety of different flowimpedance values at different points or areas of the tubular portion140. In an embodiment, the flow impedance of different portions locatedon the same cross-section normal to the axis of the tubular portion 140have substantially the same value while the flow impedance of differentportions located on the same line parallel to the axis of the tubularportion 140 may be different. Described in a different manner, in anembodiment, the flow impedance of different portions may depend on axialposition (vary based on axial position) and be independent of radialposition (have the same value on any cross-section normal to the axis).Alternatively, in an embodiment, the flow impedance of differentportions may vary based on both axial position and radial position.

The impedance distribution may be determined to transform a constantsurface fluid pressure incident on the outside of the tubular portion140 to a non-constant fluid pressure distribution on the surface of thecore sample 102 when fluid is flowing. In some contexts, the impedancedistribution may be defined by an impedance map. The impedance map maydefine an impedance value corresponding to each portion, or part, orarea of the tubular portion 140. In an embodiment, the impedance map maybe considered to have three dimensions, an axial domain dimension, aradial domain dimension, and an impedance range dimension. The axialdomain may take values from 0 to the length of the core sample 102, forexample from 0 inches to 24 inches, in the case where the length of thecore sample is 24 inches long. The radial domain may take values from 0degrees to 360 degrees, from 0 radians to 2π radians, or some otherknown angular unit. As is known to those of skill in the art, the 0degree and the 360 degree positions coincide, and the 0 radians and the2π radians positions coincide, as the circular cross-section of thetubular portion 140 is cyclical. In an embodiment, the infinite numberof points on the surface of the tubular portion 140 may be abstracted asa finite number of portions, areas, or parts of the surface. The numberof portions, areas, or parts into which the tubular portion 140 may beabstracted may be determined by one skilled in the art and may be basedon the methods employed to manufacture the tubular portion 140. Greaternumbers of portions may provide more finely resolved modeling of thedownhole environment but may also entail greater complexity ofmanufacturing and/or of design. Fewer numbers of portions may provideless resolved modeling of the downhole environment but may be easier tomanufacture and/or design.

A flow impedance value corresponding to a portion of the tubular portionmay be calculated as:

$\begin{matrix}{z = {\frac{P}{v} \propto \frac{t}{k}}} & \left( {{Eq}.\mspace{14mu} 1} \right)\end{matrix}$

where z is the flow impedance at the subject portion, v is the estimatedfluid velocity across the boundary of a virtual surface of the rock inthe subterranean formation that the core sample 102 is intended tosimulate after perforation, and P is the pressure difference at thesubject portion between the estimated formation fluid pressure prior toperforation and the estimated pressure at the boundary of thecorresponding volume after perforation. How these velocities andpressures may be estimated is discussed further below. In the right handproportion, k is the permeability at the subject portion and t is thethickness of the subject portion. Because the subject portion may beextended in length and width, some of the parameters above may varyacross points of the subject portion, and in this case an average of theparameter across the subject portion may be used. In an alternativeform, design impedance may be calculated as:

$\begin{matrix}{z = {c\frac{t}{k}}} & \left( {{Eq}.\mspace{14mu} 2} \right)\end{matrix}$

where z, t, and k are as defined with reference to Eq. 1, and where c isa proportionality constant that will be readily determined by oneskilled in the art, based on the units employed and based on the subjectfluid viscosity. The calculations to determine impedance may beperformed at every portion to define a complete impedance map that canbe used to manufacture the tubular portion 140 so that correspondingportions of the tubular portion 140 have the flow impedance defined bythe impedance map.

Turning now to FIG. 3, an alternative embodiment of the tubular portion140 is described. In an embodiment, the tubular portion 140 may bemanufactured or constructed as a sheet and rolled around the core sample102. The tubular portion 140 may be adhered to the core sample 102 at alimited number of points or secured to the core sample 102, for exampleusing snap rings, clamps, wires, strings, and/or other attachinghardware. Alternatively, the tubular portion 140 may be secured to thecore sample 102 by a support sleeve that is highly permeable andfunctions to hold the impedance sleeve 104 in place and mitigate fluidinfiltrating under the ends of the tubular portion 140. After thetubular portion 140 is attached to the core sample 102, the cap portion142 may be attached to the core sample 102.

Turning now to FIG. 4A, FIG. 4B, and 4C, an embodiment of the tubularportion 140 is described. The tubular portion 140 may be manufactured byoverlaying a plurality of strips of filter material over a single sheetof filter material. For example, strips of filter paper may be overlaidat bands b₁ through b₈. As illustrated, each single strip of filtermaterial may have the same impedance, the thickness of bands b₃ and b₄may be 4, the thickness of bands b₁, b₂, and b₅ may be 3; the thicknessof bands b₆ and b₇ may be 2; and the thickness of band ₈ may be 1, wherethe units of thickness are abstracted away and a thickness of 1corresponds to a single layer of the selected filter material. Oneskilled in the art will readily appreciate that by thoughtful selectionof a filter material having a specified impedance and by layering stripsof that filter material as illustrated in FIG. 4A, a tubular portion 140may be manufactured that has different flow impedance at differentportions of the tubular portion 140. Additionally, the strips may beformed from filter material having different impedance. For example, thetubular portion 140 may be assembled from varying numbers of stripsformed from a first filter material having a first impedance, a secondfilter material having a second impedance, and a third filter materialhaving a third impedance. By varying the number of layers of strips andvarying the impedance of strips by using different filter materials, arange of impedance values can be achieved.

It will be appreciated that the impedance distribution of the tubularportion 140 is associated with and/or related to the ratio of the localsleeve thickness to the local permeability. For a tubular portion 140manufactured from a material of a uniform permeability, the impedancedistribution would be proportional to the local thickness. It isunderstood that permeability is inversely proportional to impedance,thus a filter material having uniform impedance likewise has uniformpermeability. Additionally, given a filter material impedance and athickness of the filter material, a permeability of the filter materialmay be determined; and given a filter material permeability and athickness of the filter material, an impedance of the filter materialmay be determined.

In FIG. 4B, a tubular portion 140 is illustrated whose flow impedancevalues depend and/or vary based only on axial position. Flow impedanceat different axial positions may be different, depending on the layersof strips of filter material and the impedance of the possibly differentfilter materials used to build up layers of strips. If the tubularportion 140 is traversed circumferentially, remaining at the same axialposition, the same numbers of strips of filter material are traversedand hence the impedance value would remain the same.

The idea of building up the tubular portion 140 by layering strips canbe extended to three dimensions, so a strip may be composed of aplurality of squares or rectangles, as illustrated in FIG. 4C. In thetubular portion 140 illustrated in FIG. 4C, impedance can be made to bedifferent at each rectangle, and hence the impedance may vary with bothaxial position and radial position. In some embodiments the increasedcomplexity of manufacturing the tubular portion 140 as a plurality ofsquares or rectangles as illustrated in FIG. 4C may not providesufficient benefit versus the simpler manufacturing process involved inmaking the tubular portion 140 as a plurality of strips as illustratedin FIG. 4B. In an embodiment, the portions of FIG. 4C may be formed ofother shapes, for example, rhomboidal shapes or hexagonal shapes.

Turning now to FIG. 5, a core sample 102 having the form of anelliptical cylinder is described. The major radius of the core sample102 as illustrated is in the direction of a₁ and the minor radius is inthe direction of a₂. In an embodiment, the ratio of the major radius tothe minor radius can be designed to provide a desired variation of fluidpressure that varies with radial position in accordance with the coresample's permeability anisotropy. Using the core sample 102 having theform of an elliptical cylinder may allow testing to be conducted usingthe more simply manufactured tubular portion 140 of FIG. 4B while stillproviding the enhanced realism of varying fluid pressure in both axialand radial domains. For example, at an interior of the core sample 102having a circular cross section, there will be more core material topass through inwards along the major radius of the ellipticalcross-section than on the path inwards along the minor radius of theelliptical cross-section. This difference in path length may bedesigned, by controlling the length of the major radius and the minorradius of the elliptical cross-section during lathing of the core sample102, so as to provide the desired pressure distribution on an interiorvirtual surface of the core sample, where the interior virtual surfacecorresponds to the circular cylinder form that is used currently intypical core sample testing.

Turning now to FIG. 6A and FIG. 6B, a compliance sleeve 170 isdescribed. The compliance sleeve 170 may be inside of the impermeablebladder discussed above with reference to FIG. 1 and surrounding theimpedance sleeve 104 and/or proppant. Alternatively, in an embodiment,the compliance sleeve 170 may replace the impermeable bladder and mayitself be substantially impermeable. The compliance sleeve 170 isdesigned to have mechanical compliance or springyness that varies arounda cross-section of the compliance sleeve 170 that is normal to the axisof the core sample 102. Expressed differently, the compliance sleeve 170is designed to have mechanical compliance that varies radially and isconstant axially. As noted above, mechanical compliance can be definedas the inverse of mechanical stiffness. The compliance sleeve 170transfers the uniform forces applied by the uniform pressure of thefirst pressure chamber 108 to the outside surface of the compliancesleeve 170 as different forces to the outside of the impedance sleeve104 (perhaps through the optional proppant material). For example, wherethe compliance sleeve 170 is illustrated as thicker, along the axis a₁as illustrated in FIG. 6A, the compliance sleeve 170 would transferrelatively less of the incident force to the impedance sleeve 104, whilewhere the compliance sleeve 170 is illustrated as thinner, along theaxis a2 as illustrated in FIG. 6A, the compliance sleeve 170 wouldtransfer relatively more of the incident force to the impedance sleeve104. An example disposition of the compliance sleeve 170 in the testconfiguration is illustrated in FIG. 6B. The first pressure chamber 108surrounds the compliance sleeve 170. the compliance sleeve 170 surroundsa layer of proppant material 172. The proppant material surrounds theimpedance sleeve 104. The impedance sleeve 104 surrounds the core sample102. The compliance sleeve 170 may promote modeling differences betweena vertical overburden pressure and a horizontal overburden pressure,thereby enhancing the realism of the test conditions.

The compliance sleeve 170 may be made of a variety of materials. In anembodiment, the compliance sleeve 170 may be made of metal. In anembodiment, the compliance sleeve 170 may be made of an elastomericmaterial. In an embodiement, the compliance sleeve 170 may comprise anouter membrane, an inner membrane, and deformable beads sandwichedbetween the membranes such that when sufficient pressure is applied, thebeads deform. The beads may be of variable deformability and/or ofvariable size to promote a different compliance at different locationsaround the compliance sleeve 170. The compliance sleeve 170 may be madeof other materials.

Turning now to FIG. 7, a first core sample test fixture 188 isdescribed. The first core sample test fixture 188 comprises a first pairof actuators 190 a, 190 b that apply forces in opposite direction toeach other along a first axis and a second pair of actuators 192 a, 192b, that apply forces in opposite direction to each other along a secondaxis, wherein the first axis is normal, perpendicular, and/or orthogonalto the second axis. The first core sample test fixture 188 furthercomprises curved plates 194, 196, 198, and 200 through which theactuators 190 a, 190 b, 192 a, and 192 b, respectively, apply force tothe impedance sleeve 104 and the core sample 102. The first core sampletest fixture 188 further comprises a fourth pump 202, a fifth pump 204,and a controller 206. The fourth pump 202 is plumbed via tubing to thefirst pair of actuators 190 a, 190 b. The fifth pump 204 is plumbed viatubing to the second pair of actuators 192 a, 192 b. The two pairs ofactuators 190 a, 190 b, 192 a, 192 b may be driven with differenthydraulic pressures to apply a different force to the core sample 102 inthe vertical axis from the force applied to the core sample 102 in thehorizontal axis. The controller 206 may control the fourth and fifthpumps 202, 204 to provide the commanded or predefined force to the coresample 102. In an alternative embodiment, a single hydraulic pump may beemployed to provide hydraulic pressure, and the controller 206 maymodulate control valves to control the hydraulic pressure supplied tothe actuators 190 a, 190 b, 192 a, 192 b. The controller 206 maymodulate the control valves to supply different hydraulic pressures tofirst pair of actuators 190 a, 190 b versus the second pair of actuators192 a, 192 b. In an alternative embodiment of the first core sample testfixture 188, the actuators 190 a, 190 b, 192 a, 192 b may beelectrically actuated, and the controller 206 may control electricmotors that provide motive force.

Turning now to FIG. 8, a second test fixture 210 is described. Thesecond test fixture 210 comprises a containment 212, a piston 214, and amaterial 216. The material 216 may comprise gravel, sand, proppant,beads, or other material. The core sample 102 is surrounded by thematerial 216 within the containment 212. The core sample 102 for use inthe second test fixture 210 may be a generally rectangularcross-section, as illustrated in the end view of FIG. 8, and may begenerally a rectangular prism measuring about 4 inches by 4 inches byabout 24 inches. Alternatively, the core sample 102 for use in thesecond test fixture 210 may be generally a rectangular prism measuringabout 6 inches by 6 inches by about 24 inches. By applying force to thepiston 214, the piston 214 displaces within the containment 212 totransfer the force to the top of the core sample 102 via the material216.

The force may be applied to the piston 214 from a fluid or gas pressureintroduced into the upper chamber. Alternatively, the force may beapplied to the piston 214 from an actuator, such as a hydraulic actuatoror an electric actuator. Although the material 216 may flow freelywithin the containment 212, the force applied to the core sample 102 bythe material 216 may be greater in the vertical direction than in thehorizontal direction. In an embodiment, the side walls of thecontainment 212 may be spring loaded and/or incorporate springs thatgive way slightly to reduce the horizontal component of the forcetransferred to the side of the core sample 102. The forces applied tothe core sample 102 by the material 216 may simulate and/or model theeffect of overburden pressure in a downhole environment. Fluid flow isfree to flow around the material 216 and to apply fluid pressure to thecore sample 102 that simulates and/or models formation fluid pressure inthe downhole environment. The second test fixture 210 may be combinedwith aspects of the previously described innovations. For example, theimpedance sleeve 104 described above may be employed when testing thecore sample 102 using the second test fixture 210. One skilled in theart would readily be able to adapt the embodiments of the impedancesleeve 104 illustrated in FIG. 4A, FIG. 4B, and FIB 4C to therectangular prism core sample 102 associated with the second testfixture 210.

Turning now to FIG. 9, a method 220 is described. At block 222,pre-testing is performed to determine perforation geometry andperforation damage. Pre-testing may follow guidance provided by API RP19B. Pre-testing may involve conducting one or more preliminary testsand examining the core samples 102 after the preliminary tests. At block224, a pressure distribution and a velocity distribution may becalculated based on the pre-test results and/or based on downholeoperational parameters. The pressure distribution comprises theestimated values of pressure after perforation at different points on avirtual surface of the rock in the subterranean formation that the coresample is intended to simulate. Downhole, as fluid flows into theperforation tunnel in the formation, it is thought that the formationpressure at a distance from the perforation tunnel drops until it equalsthe pressure in the wellbore. The velocity distribution comprises theestimated value of fluid flow velocity crossing the virtual surface ofthe rock in the subterranean formation that the core sample is intendedto simulate. The pressure distribution and the velocity distribution maybe calculated by a variety of methods known to those skilled in the art.For example, the pressure distribution and velocity distribution may becalculated based on methods described in pages 145 through 158, inComputer Aided Optimum Design of Structures VIII, by James E. Brooks,published by WIT Press, 2003.

Downhole operational parameters may comprise one or more formationparameters, one or more perforation parameters, one or more wellboreparameters, and one or more core sample parameters. The formationparameters comprise rock permeability, rock type, overburden pressure,formation pressure, reservoir diameter, and reservoir height. Theperforation parameters comprise penetration length, penetration shape,penetration damage, shot density, and gun phasing. The wellboreparameters comprise wellbore diameter, wellbore pressure, casingthickness, casing material, cement thickness, and cement type. The coresample parameters comprise core sample length and core sample diameter.One skilled in the art will appreciate that there may be otherparameters that may be taken into consideration, depending upon thelevel of analysis elaboration and precision of test results desired.There is typically a trade off between increasing numbers of parametersand more detailed analysis versus complexity and time of completing thetesting procedure.

At block 226 an impedance map is determined based on the downholeoperational parameters. In an embodiment, the impedance may bedetermined based on the pressure distribution and the velocitydistribution determined above at block 224. The impedance may bedetermined at every element of the impedance map using Eq. 2 describedabove. Thus, the impedance at an element is equal to the quotient of thepressure associated with the subject element by the pressuredistribution divided by the fluid velocity associated with the subjectelement by the velocity distribution multiplied through by theappropriate proportionality constant to adapt to the units employed.This calculation may be performed for every element of the impedancemap. The impedance map may be conceived to have a domain in a firstdimension whose values correspond to displacement along the length ofthe axis of the core sample 102, a domain in a second dimension whosevalues correspond to displacement around the circumference of thecross-section of the core sample 102 (which may be referred to in somecontexts as radial displacement), and a range in a third dimension whosevalues are the impedance associated with that location of the impedancemap. The impedance map may be partitioned into a finite number ofelements, for example, the impedance map may be partitioned ordiscretized into an eight-by-eight, sixty-four element map thatcorresponds to sixty-four portions of the tubular portion 140. Theimpedance map may be partitioned into any number of elements. The axialdomain of the impedance map may be partitioned into any number ofincrements. The radial domain of the impedance map may be partitionedinto any number of increments. A tubular portion 140 having sixty-fourportions is illustrated in FIG. 4C. The impedance value of each mapelement, and hence the corresponding portion of the tubular portion 140,may have a different value from every other map element. Expressed in adifferent way, the impedance value of each map element may beindependent of every other map element. In some embodiments, dependingon operational parameters, some map elements may have substantiallyequal impedance values.

In one embodiment, the impedance of portions of the tubular portion 140are of substantially equal value for all portions associated with thesame position along the axis of the core sample 102, for example in thiscase the impedance map may be two dimensional. In this case, impedancevalues may have a different value for different values of the axialdomain, but for any selected value of the axial domain, the impedanceremains substantially equal at different values of the radial domain.For example, the impedance map may be partitioned into an eight elementmap that corresponds to eight portions of the tubular portion 140. Atubular portion 140 having eight portions is illustrated in FIG. 4B.

The impedance values in the impedance map, either three dimensional ortwo dimensional, may likewise be constrained to a discrete range ofvalues. For example, the range of impedance values may be constrained tofour different values, eight different values, twelve different values,or some other suitable number of values. Discretizing the impedancevalues may promote ease of manufacturing the tubular portion 140 and theimpedance sleeve 104 generally.

At block 228, a sleeve is manufactured based on the impedance map. Thesleeve may be manufactured from layers of filter material, for examplefilter paper, or from a ceramic material. Alternatively, the sleeve maybe manufactured as a filter cake comprised of fine particle matter, suchas fie silt, fine sand, fine clay, and/or other fine particle matter. Inan embodiment, the sleeve may be manufactured to have impedance varyingonly over the axial domain and not varying over the radial domain, asillustrated in FIG. 4B. In this case, a three dimensional impedance mapmay be used, for example by using an average of impedance values at thesame value in the axial domain, or alternatively a two dimensionalimpedance map may be used.

In an embodiment, the sleeve may correspond to the impedance sleeve 104described above. Alternatively, the sleeve may correspond to the tubularsection 140 described above. At block 230, the sleeve is attached to thecore sample 102. In an embodiment, the sleeve may be secured to the coresample 102, for example using snap rings, clamps, wires, strings, and/orother attaching hardware. The flow impedance of each of a plurality ofportions of the sleeve is based on the impedance map. At block 232,optionally the cap portion 142 is attached to the core sample 102 or tothe tubular portion 140 of the impedance sleeve 104. The cap portion 142has a predetermined flow impedance. The flow impedance of the capportion 142 may vary from the center of the cap portion 142 out to theedges of the cap portion 142, for example having a greater flowimpedance towards the curved perimeter of the cap portion 142 and alesser flow impedance towards the center of the cap portion 142. Atblock 234, an optional support sleeve is attached over the sleeve. Thesupport sleeve, as described above, may function to hold the sleeve inplace and mitigate fluid infiltrating under the ends of the sleeve.

At block 236, the core sample is perforated, for example by detonatingthe explosive charge 116. At block 238, the flow performance of the coresample 102 is measured. It is understood that throughout the method 220,various pressures, pressure transients, fluid flows, and otherparameters may be measured and recorded for later analysis. The resultsof analysis of the data gathered from testing the core sample 102 may beused to refine and elaborate the test parameters, and method 220 may beperformed iteratively to refine and elaborate perforation parameters.

Turning now to FIG. 10 a method 250 is described. At block 252, the coresample 102 enclosed by a sleeve is tested, wherein a flow impedance ofeach of a plurality of portions of the sleeve is based on a impedancemap, and the flow performance of the core sample 102 is measured. Theprocessing of block 252 may correspond substantially to one or more ofthe steps of method 220 described above with reference to FIG. 9. Atblock 254, based on the flow performance measured pursuant to the testof the core sample 102, determine perforation design parameters.Perforation design parameters may include one or more of shots per feet(density of shots), charge phasing, and the design of the explosivecharge 116. Explosive charges 116 can be designed to release more orless energy; to direct their explosive energy with a relatively narroweror broader focus; to have different liner designs. An angle of theexplosive charges 116 as determined by their mounting in the perforationgun, can be varied. At block 256, assemble a perforation gun based onthe perforation design parameters.

At block 258, the perforation gun is run into a wellbore to designdepth, for example a desired production depth. The perforation gun mayhave been at least partially assembled in a shop and transported to thewellbore location. Any remaining assembly of the perforation gun may becompleted at the wellbore location, such as removing detonationsafeties, installing detonators, and/or other final assembly steps. Atblock 260, optionally under balance or over balance wellbore pressureconditions may be established, for example by setting packers andapplying appropriate pressure down a tubular string. At block 262, theperforation gun is fired, perforating the wellbore.

Turning now to FIG. 11, a wellbore servicing system 310 is described.The system 310 comprises a servicing rig 316 that extends over andaround a wellbore 312 that penetrates a subterranean formation 314 forthe purpose of recovering hydrocarbons, storing hydrocarbons, disposingof carbon dioxide, or the like. The wellbore 312 may be drilled into thesubterranean formation 314 using any suitable drilling technique. Whileshown as extending vertically from the surface in FIG. 11, in someembodiments the wellbore 312 may be deviated, horizontal, and/or curvedover at least some portions of the wellbore 312. The wellbore 312 may becased, open hole, contain tubing, and may generally comprise a hole inthe ground having a variety of shapes and/or geometries as is known tothose of skill in the art.

The servicing rig 316 may be one of a drilling rig, a completion rig, aworkover rig, a servicing rig, or other mast structure and supports aworkstring 318 in the wellbore 312, but in other embodiments a differentstructure may support the workstring 318, for example an injector headof a coiled tubing rigup. In an embodiment, the servicing rig 316 maycomprise a derrick with a rig floor through which the workstring 318extends downward from the servicing rig 316 into the wellbore 312. Insome embodiments, such as in an off-shore location, the servicing rig316 may be supported by piers extending downwards to a seabed.Alternatively, in some embodiments, the servicing rig 316 may besupported by columns sitting on hulls and/or pontoons that are ballastedbelow the water surface, which may be referred to as a semi-submersibleplatform or rig. In an off-shore location, a casing may extend from theservicing rig 16 to exclude sea water and contain drilling fluidreturns. It is understood that other mechanical mechanisms, not shown,may control the run-in and withdrawal of the workstring 318 in thewellbore 312, for example a draw works coupled to a hoisting apparatus,a slickline unit or a wireline unit including a winching apparatus,another servicing vehicle, a coiled tubing unit, and/or other apparatus.

In an embodiment, the workstring 318 may comprise a conveyance 330, aperforation tool 332, and other tools and/or subassemblies (not shown)located above or below the perforation tool 332, for example a surgesub-assembly, one or more packers, and other sub-assemblies. Theconveyance 330 may comprise any of a string of jointed pipes, aslickline, a coiled tubing, a wireline, and other conveyances for theperforation tool 332. In an embodiment, the perforation tool 332comprises one or more explosive charges that may be triggered toexplode, perforating a casing if present, perforating a wall of thewellbore 312 and forming perforations or tunnels out into thesubterranean formation 314. The perforating may promote recoveringhydrocarbons from the subterranean formation 314 for production at thesurface, storing hydrocarbons flowed into the subterranean formation314, or disposing of carbon dioxide in the subterranean formation 314,or the like.

While several embodiments have been provided in the present disclosure,it should be understood that the disclosed systems and methods may beembodied in many other specific forms without departing from the spiritor scope of the present disclosure. The present examples are to beconsidered as illustrative and not restrictive, and the intention is notto be limited to the details given herein. For example, the variouselements or components may be combined or integrated in another systemor certain features may be omitted or not implemented.

Also, techniques, systems, subsystems, and methods described andillustrated in the various embodiments as discrete or separate may becombined or integrated with other systems, modules, techniques, ormethods without departing from the scope of the present disclosure.Other items shown or discussed as directly coupled or communicating witheach other may be indirectly coupled or communicating through someinterface, device, or intermediate component, whether electrically,mechanically, or otherwise. Other examples of changes, substitutions,and alterations are ascertainable by one skilled in the art and could bemade without departing from the spirit and scope disclosed herein.

1. A method of testing a core sample, comprising: determining an impedance map; attaching a sleeve to the core sample, wherein a flow impedance of each of a plurality of portions of the sleeve is based on the impedance map; and measuring a flow performance of the core sample.
 2. The method of claim 1, wherein the impedance map is determined based on at least one of a formation parameter, a perforation parameter, a wellbore parameter, and a core sample parameter.
 3. The method of claim 2, wherein the formation parameter comprises one of a rock permeability, a rock type, an overburden pressure, a formation pressure, a reservoir diameter, and a reservoir height; wherein the perforation parameter comprises one of a penetration length, a penetration shape, a penetration damage, a shot density, and a gun phasing; wherein the wellbore parameter comprises one of a wellbore diameter, a wellbore pressure, a casing thickness, a casing material, a cement thickness, and a cement type; and wherein the core sample parameter comprises one of a core sample length and a core sample diameter.
 4. The method of claim 1, wherein portions of the sleeve that are equal distance from an end of the core sample have the same flow impedance.
 5. The method of claim 4, further comprising: determining an elliptical cross section based on a rock permeability; and shaping the core sample to have the determined elliptical cross section.
 6. The method of claim 1, wherein at least two portions of the sleeve that are equal distance from an end of the core sample have different flow impedance and wherein at least two portions of the sleeve that are at different distances from an end of the core sample have different flow impedance.
 7. The method of claim 1, further comprising: determining a pressure differential associated to each of the portions of the sleeve based on at least one of a formation parameter, a perforation parameter, a wellbore parameter, and a core sample parameter; determining a flow velocity associated to each of the portions of the sleeve based on at least one of a formation parameter, a perforation parameter, a wellbore parameter, and a core sample parameter, and wherein the impedance map is determined at least in part based on the pressure differentials associated to each of the portions of the sleeve and based on the flow velocities associated to each of the portions of the sleeve.
 8. The method of claim 1, further comprising modifying a pressure transient that occurs after the core sample is perforated, where the pressure transient is modified by fluid flow into an interior of a surge device, wherein the surge device comprises a piston, an interior chamber, and a crushable spring, wherein the piston mass, the volume of the interior chamber, and the spring constant of the crushable spring are designed to produce the modified pressure transient.
 9. A perforation test target, comprising: a metal plate; a core sample adhered to the metal plate at one end; and a first sleeve adhered to the core sample, wherein a flow impedance of each of a plurality of portions of the first sleeve is based on a predetermined impedance map.
 10. The perforation test target of claim 9, wherein the first sleeve is comprised of layers of filter paper, wherein the number of layers at each portion of the first sleeve corresponds to the flow impedance at that portion.
 11. The perforation test target of claim 9, wherein the first sleeve is comprised of ceramic material, wherein the geometry of the first sleeve is based on the predetermined impedance map.
 12. The perforation test target of claim 9, further comprising a second sleeve positioned over the first sleeve, wherein a compliance of the second sleeve varies along a circumference of the core sample.
 13. The perforation test target of claim 9, wherein the perforation test target further comprises a cap adhered to an end of the core sample opposite the metal plate, wherein the cap has a flow impedance based at least on one of a formation parameter, a perforation parameter, a wellbore parameter, and a core sample parameter.
 14. A system for testing a core sample, comprising: a non-permeable sleeve placed over the core sample; a first pair of opposing actuators to apply opposing force to the non-permeable sleeve in a first axis normal to the axis of the core sample; a second pair of opposing actuators to apply opposing force to the non-permeable sleeve in a second axis normal to the axis of the core sample and normal to the first axis; a wellbore pressure reservoir to provide simulated wellbore pressure; and a formation pressure reservoir to provide simulated formation fluid pressure.
 15. The system of claim 14, wherein the first pair of opposing actuators and the second pair of opposing actuators are hydraulic actuators.
 16. The system of claim 14, wherein the first pair of opposing actuators and the second pair of opposing actuators are electrical actuators.
 17. The system of claim 14, wherein the force applied by the first pair of opposing actuators and the second pair of opposing actuators are separately controlled, wherein the force applied to the core sample by the first pair of opposing actuators is based on a vertical overburden pressure, and wherein the force applied to the core sample by the second pair of opposing actuators is based on a horizontal overburden pressure.
 18. The system of claim 14, further comprising a core sample, wherein the core sample has the shape of an elliptic cylinder.
 19. The system of claim 14, further comprising a permeable sleeve adhered to the core sample, wherein the non-permeable sleeve is positioned over both the permeable sleeve and the core sample, wherein a flow impedance of each of a plurality of portions of the permeable sleeve is based on an impedance map, wherein the impedance map is determined based on at least one of a formation parameter, a perforation parameter, a wellbore parameter, and a core sample parameter.
 20. The system of claim 19, wherein the permeable sleeve is comprised of one of filter material, filter cake, and ceramic. 